Gate CS 2023 | Question - 32 | Digital Logic

Here's how you can approach the problem:

• The number given in radix-4 is 132.
• Convert this number to decimal:
  = (1×4²) + (3×4¹) + (2×4⁰)
  = 16 + 12 + 2 = 30
• Now, convert the decimal number 30 to radix-5.

To convert the decimal number to radix-5, we divide the decimal number by 5 repeatedly, keeping track of the remainder. The remainders, read in reverse order, give the equivalent number in radix-5.

• 30 ÷ 5 = 6, remainder 0
• 6 ÷ 5 = 1, remainder 1
• $1÷5=\mathrm{0,}$remainder 1

So, the radix-5 representation is 110.